Given v⃗ 𝑣→ with an initial point of ⟨−1,4,6⟩⟨−1,4,6⟩ and a terminal point of ⟨3,3,8⟩⟨3,3,8⟩ , find a unit vector in the same direction as v⃗ 𝑣→.Please be sure your final answer has all denominators rationalized.

To find a unit vector in the same direction as vector v, we first need to find the vector v. The vector v is found by subtracting the initial point from the terminal point.

So, vector v = ⟨3-(-1), 3-4, 8-6⟩ = ⟨4, -1, 2⟩

Next, we find the magnitude (or length) of vector v. The magnitude is found by taking the square root of the sum of the squares of the components.

Magnitude of v = √(4^2 + (-1)^2 + 2^2) = √(16 + 1 + 4) = √21

Finally, to find the unit vector in the same direction as v, we divide each component of v by the magnitude.

Unit vector = ⟨4/√21, -1/√21, 2/√21⟩

To rationalize the denominators, we multiply the numerator and denominator by √21.

Unit vector = ⟨4√21/21, -√21/21, 2√21/21⟩

So, the unit vector in the same direction as v is ⟨4√21/21, -√21/21, 2√21/21⟩.